Cut eggplant into 1/4-inch thick slices, place in single layer in colander, sprinkle with salt and allow to drain for 30 minutes (during this time prepare the meat sauce). Rinse off salt then press slices between paper towels, removing as much excess moisture as possible. Dip each slice in beaten egg and then breadcrumbs. Pan fry slices in olive oil until browned on each side. Reserve.

Boil potatoes until just fork tender. Allow to cool. Remove skins, cut into 1/4-inch thick slices. Reserve.

Grate Parmesan cheese and reserve.

In a 12-inch skillet over medium heat, saute onion in olive oil until translucent, add in garlic and saute another minute. Add in lamb and seasonings and cook until meat is cooked through. Add in tomato paste and wine, cook for an additional 5 minutes. Reserve.

In a medium heavy bottom sauce pan over medium-low heat, melt butter. Once completely melted whisk in flour until well blended. Slowly pour in milk, whisking continuously as the sauce will become very thick until all milk is incorporated. Increase the temperature to medium and add in the salt and nutmeg.

To temper the egg yolks so they won't scramble when added to the hot sauce, beat egg yolks in a separate bowl and add a ladle of sauce to the yolks WHILE whisking. Once combined pour egg mixture back into sauce and whisk well. Reduce the heat to the lowest temperature, do not allow to boil.

Preheat oven to 350 degrees. Coat an 11x7 or 9x9 pan with cooking spray.

Line the bottom of the pan with a single layer of potato slices, overlapping slightly. Top with a layer of eggplant slices, then add the meat sauce, top that with any additional eggplant slices. Sprinkle with half of the Parmesan cheese. Ladle the bechamel sauce generously on top, then sprinkle with remaining cheese.

Bake for 35 - 45 minutes until top is golden brown. Allow to rest at least 10 mnutes before serving.